Secular Bar-mode Instability in Rapidly Rotating Neutron Star

First run of the ROT181 model

The following is the result of the simulations on the ROT181 model.

Movies for the f-mode simulation performed on LSU's Beowulf cluster Super Mike
Initial model	Resolution	# of processors	computer	plots	movies	comments
\beta=0.181	13098128	64 Pentium 4	LSU Super Mike	j22_1, j22_2, angmom, \beta, high order modes, D22 * \omega^5	top movie, side movie	The \kappa = 2*10^5, we fourier transform the density array and plot both \cos and \sin coefficients for each m mode at r=0.24, z=0.0.

In the above simulation, we observe some higher order modes grow up at the final stage. We first suspect this is a GR effect due to the large fudge factor, but the fact that the loss of the angular momentum slows down suggest that the GR effect at the final stage is not as strong as we expected. Notice that in the expression of the GR potential, the only time dependence comes from the fifth time derivative of the quadrupole moment, if we have a pure eigen mode, then the GR potential is proportional to ( \D22 \times \omega^5). As time goes on, the quadrupole moment grows up and stable at some value, after some time, it starts to decrease. On the other hand, the frequency of the mode stablizes at some value then starts to drop after the bar is well formed. In order to see how the GR potential changes with time, we plotted ( \D22 \times \omega^5) against time which in some sense shows the strength of the GR potential. This plot actually shows that the strength of the GR potential peaks at t=8 rotational periods and decreases significantly at the final stage (the last several peaks are most likely introduced by the mixture of higher order modes), thus we suspect this instability is not caused by the GR effect but a pure hydrodynamical effect. We decided to shut off the GR term from t=12 rotational periods, repeat the simulation to see if this instability happens.

Movies for the GR off run to test the dynamical pear mode instability
Initial model	Resolution	# of processors	computer	plots	movies	comments
\beta=0.181 after 12 rotational periods	13098128	64 Pentium 4	LSU Super Mike	j22_1, j22_2, angmom, \beta, high order modes, D22 * \omega^5	top movie	we shut off the GR reaction to see if the pear mode is a GR effect or a pure hydrodynamical effect. This run only went 2 spin periods, but the odd modes are already noticeable.

Second run of the ROT181 model

Movies for the new run on helix using a better way to handle the center of mass
Initial model	Resolution	# of processors	computer	plots	movies	comments
\beta=0.181	13098128	32 Pentium 4	LSU Super Helix	j22_1, j22_2, angmom, \beta, high order modes, D22 * \omega^5	top movie, side movie	we restart our simulation after implementing an more elegant way to control the center of mass motion. This run confirms the new instability.

Movies for the new run on helix with GR effect off
Initial model	Resolution	# of processors	computer	plots	movies	comments
\beta=0.181 after 11 rotational periods	13098128	32 Pentium 4	LSU Super Helix	j22_1, j22_2, angmom, \beta, high order modes, D22 * \omega^5	top movie, side movie	we shut off GR effect to see if the odd modes will grow. They does grow up.